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Primary National Strategy – Pete

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					    Theme: mental strategies for addition and subtraction (addition and subtraction progression document) framework document

    Objectives from the new framework:


Reception: Begin to relate addition to combining two groups of objects and subtraction to ‘taking away’
Year 1: Recognise that addition can be done in any order and use this to add mentally a one-digit number or a multiple of 10 to a one-digit or two-digit
number
Subtract one-digit numbers from one-digit and two-digit numbers and a multiple of 10 from a two-digit number; apply addition and subtraction strategies,
e.g. counting on to find the difference
Year 2: Add or subtract mentally a single-digit number or a multiple of 10 to or from any two-digit number; use practical and informal written methods to
support addition and subtraction of two-digit numbers
Year 3: Add or subtract mentally combinations of one-digit and two-digit numbers
Year 4:Add or subtract mentally pairs of two-digit whole numbers, e.g. 47 + 58, 91 – 35
Year 5:Use mental methods to add and subtract 2 or more 2, 3 or 4 digit numbers-special cases, e.g. look for number bonds to 10/100 or count on when
subtracting numbers near multiples of 100, 1000, e.g. 1995 from 6007
Year 6: Calculate mentally with whole numbers and decimals, e.g. U.t ± U.t
Year 6 extension: Consolidate and extend mental methods of calculation
                                                            Key Resources /
Year Target         Group Target                                                     Outcomes
                                                            Models and Images
                            Add and subtract numbers        Unit plans:              Most pupils should be able to:                          Put 1, 2 or 3 in each circle so that each
                            below 10                        Autumn unit 4            What is seventeen subtract five?                        side adds up to 5. You can use each
Yr 1                m                                       Autumn unit 9                                                                    number as often as you like.
                                                            Spring unit 3            Add five and eight?                                     Find different ways of doing it.
                            Add and subtract numbers                                 How many different ways can you score 4 by
Calculate                   below 20                        ICT files                rolling two dice? What about 6?
efficiently and     s
accurately                                                  Excel files              Explain strategy for solving:
                            Add or subtract mentally a                               4 + 7; 5 add 6; 11 subtract 4; 18 + 5;9 less than 17;
Further                                                     Problem solving          12 minus 8
examples of                 single-digit number or a
                            multiple of 10 to or from any   materials:
pitch and                                                                            Add or subtract without crossing 10/20 boundaries,
expectations:               two-digit number;                                                                                                Lisa has 5 pens and Tim has 2 pens.
                                                            Gobstopper               e.g. solve problems such as :                           How many pens do they have altogether?
                                                            Bens numbers                                                                     How many more pens has Lisa than Tim?
Foundation to                                               Caterpillar sequences     - 3 = 4, 17 -  = 12
year 1                                                      Down path                                                                        Anil spent 6p and 3p on toffees.
                                                            Lollipops                Put the numbers 1 to 4 in the circles so that the       What change from 10p did he get?
Further                                                     Bowling                  difference between each pair of joined numbers is
examples of                                                 Pick a pair              more than 1.
pitch and                                                                                                                                    It is 5 o’clock.
expectations:                                                                                                                                What time will it be 4 hours from now?
                                                                                                                                             What time was it 3 hours ago?
                                                            20 Bead strings          Look at these cards.                                    If you had tea at 3 o’clock, how long ago
Year 1                                                      Stories (e.g. Walter’s
                                                                                       3          1         4            2       6           was that?
                                                            Windy Washing line by                                                            If you go to bed at 8 o’clock, how many
Further                                                     Neil Griffiths)
Information                                                                                                                                  hours until bed time?
                                                                                     Use one card each time to make these correct.
- Divide and        c                                       Number lines
rule1                                                       Number tracks              7      +                 =   10
                                                            (including those
- Divide and                                                marked on the
rule2                                                       playground)                       -                 =
                                                                                      10                            4
                                                            Carpet Tiles
- teaching                                                  100 Bead bar
mental                                                                               Tick (   ) two numbers which add up to 17.
calculation
strategies                                                                                                               5
                                                                                                                                             How many children did we ask?
- teaching                                                                                                                                   How many children liked more children
written                                                                                                         8            6
                                                                                                                                             liked chocolate than lime?
strategies
                                                                                                                         9
- exemplification
of standards                                                                                                                                                                  Level 1b-1a
                        Add and subtract numbers        Unit plans:               Most pupils should be able to:                         My cat is 30 cm tall.
                        below 20                        Autumn unit 3; Autumn                                                            My dog is 25 cm taller.
Yr 2                m                                   unit 9                                                                           How tall is my dog?
                                                        Spring unit 3; Summer     Quickly solve:
                                                        unit 9                                                                           James walked from 9:45 until 10:15.
Calculate               Add or subtract mentally a      20 Bead strings           5+36                                                   For how many minutes did he walk?
efficiently and         single-digit number or a        Carpet Tiles              1 +  + 5 = 17
accurately          s   multiple of 10 to or from any   Number lines & number     58+21                                                  Which two/three numbers could have a
                        two-digit number;               tracks (including those   70-11                                                  sum of 15?
                        Add or subtract mentally        marked on the             35+19
Further                                                 playground)               24-9                                                   Work mentally to complete written
examples of             combinations of one-digit and
                        two-digit numbers                                                                                                questions like:
pitch and                                                                                                                                32 + 5 = ▲; 32 + ▲ = 37; ▲ + 5 = 37
expectations:                                           ICT files                 Explain how they solved:                               86 – 4 = ▲; 86 – ▲ = 82; ▲ – 4 = 82
                                                                                  82-79
Year 2                                                  Problem solving           40+39                                                    30 + 4 = ▲; 30 + ▲ = 34; ▲ + 4 = 34
                                                        materials:                                                                         600 + 7 = ▲; 600 + ▲ = 607;
Further                                                                           Given 3 numbers, e.g. 2, 7 and 9, be able to say or write▲ + 7 = 607
                                                                                                                                            four
Information                                             Gobstopper                different number sentences linking the numbers.          and explain method.
- Divide and                                            Bens numbers
rule1                                                   Caterpillar sequences     Using three dice, find different ways of scoring 12.
                                                        Down path                                                                        Work mentally to complete written
- Divide and                                            Lollipops                 Put the numbers 1 to 5 in the circles so that the      questions like:
rule2                                                   Bowling                   difference between each pair of joined numbers is      22 – 17 = ▲       19 + ▲ = 22
                                                        Pick a pair               more than 1.                                           103 – 96 = ▲      95 + ▲ = 101
- teaching                                              Money match                                                                      64 – 58 = ▲       87 + ▲ = 94
mental                                                  Bird eggs
calculation                                             Card sharp                                                                       This table shows how the children in a
strategies                                              Monster                                                                          class come to school.
                    c                                   Sum up                                                                              Ways of coming         Number of
- teaching                                              Timetables                Respond to oral questions like:                             to school             children
written                                                 In a line                 What must be added to 30 to make 100?
strategies
                                                                                  and explain method.
                                                        Number square             • Work mentally to complete written questions like:
                                                                                                                                            walk                       14
- exemplification                                       mystery                   40 + ▲ = 100              70 + ▲ = 100
of standards                                            Beanbag buckets
                                                        Lucy Fair                 I have £14. I am given another £9.
                                                                                                                                            taxi                        1
                                                        Cross roads               How much do I have now?
                                                        Duck pond
                                                        Christmas candles
                                                                                                                                            bus                         6
                                                                                  • A pear costs 15p more than an apple.
                                                        Goldfish problem          An apple costs 12p.
                                                                                  What does a pear cost?                                    car                         8
                                                        100 Bead bar
                                                        100 Bead strings          Investigate ways of using silver coins to pay 50p.     (a)      More children walk than come
                                                                                                                                         by bus.
                                                        Laminated empty                                                                  How many more?
                                                        number lines and                                                                 (b) How many children are in the class
                                                        whiteboard pens.                                                                 altogether?

                                                                                                                                                                      Level 2c-2b
                                                             Key Resources /
Year Target         Group Target                                                       Outcomes
                                                             Models and Images
                            Add or subtract mentally a       Springboard 3 unit 6      Most pupils should be able to:
                            single-digit number or a         Y3 Autumn unit 2;         What is twenty-seven subtract nine?
                            multiple of 10 to or from any    Y3 Autumn unit 3;
                            two-digit number;                Y3 Spring unit 2          Add thirty-six and seventy

                                                             ICT files                 What is twenty-six more than fifty?

                                                             Problem solving           Subtract thirty-two from seventy.
                                                             materials:
Yr 3                m                                                                  The difference between a number and twenty-          This table shows the increase in bus fares.
                                                             Arithmagons               nine is ten. What could the number be?
                                                             Card tricks
                                                             Esmerelda coins           What is the sum of twenty-three and twenty-
                                                             Crackers                  seven?
                                                             Coin rows
                                                             Sheepdog trials           In a class there are thirty-two children. If there
                                                             Three monkeys             are twenty-three girls, how many boys are
                                                             Odds and evens            there?
                                                             Number square
                                                             mystery                   In a class of thirty-two children, fourteen
Calculate                   Add or subtract mentally                                   walked to school and the rest came by bus.
efficiently and     s       combinations of one-digit and    Snakes and ladders        How many came by bus?
accurately                  two-digit numbers                                                                                               Sohan's new bus fare is 72p. How much has
                            Add or subtract mentally pairs                             Circle three numbers that add to make a              his bus fare gone up?
Further                     of two-digit whole numbers       Hundred square            multiple of 10.                                      Millie says, 'My bus fare has gone up by 10p'.
examples of                 including crossing the                                                                                          How much is Millie's new bus fare?
pitch and                   hundreds boundary, e.g. 47 +     100 Bead bar              11 12 13 14 15 16 17 18 19
expectations:               58, 101 – 35                     100 Bead strings                                                               Put a number in the box to make this correct.
                                                                                       Each side of this square must add up to 80.                             32 + 6 = 40 - ▲
Year 3                                                       Laminated empty           Write in the missing numbers.
Further                                                      number lines and
Information                                                                                                                                 Some children made a bar chart to show
                                                             whiteboard pens.                                                               how far they could swim.
- Divide and
rule1                                                        Calculation course link                                                          Sue


- Divide and                                                                                                                                  Ann
                    c
rule2
                                                                                                                                              Kay

- teaching
                                                                                                                                              Mark
mental                                                                                 This is a number triangle with some numbers
calculation                                                                            missing. The numbers along each edge must              Paul
strategies                                                                             add up to 90.
                                                                                                                                                     10   20    30   40    50 60   70   80   90 100
- teaching                                                                             Put all the numbers 20, 30, 50 and 60 in the                                       metres
written                                                                                circles to make the totals correct.                  Sue can swim further than Anne. How
strategies                                                                                                                                  much further?
- exemplification
of standards
                                                                                                                                                                                        Level 2a-3c
                        Add or subtract mentally         Autumn: unit 2(1-3);        Most pupils should be able to:                      A box holds 70 biscuits.
                        combinations of one-digit and    unit 2(4-5); unit 3(1-2);                                                       How many biscuits are left if you eat 17
Yr 4                m   two-digit numbers                unit 3(3-5); unit 12        Carry out calculations efficiently and explain      biscuits?
                                                         Spring: unit 2; unit 3      methods, e.g.                                       How many people can have 5 biscuits each?
                                                         Summer: unit 2; unit 3;                                                         How many biscuits are there in 6 boxes?
Calculate               Add or subtract mentally pairs   unit 12                     49 + 57; 9 + 7 = 16 and 40 + 50 = 90, so 90 +       How many boxes are needed to hold 200 biscuits?
efficiently and         of two-digit whole numbers                                   16 is 90, 100, 106.
accurately          s   including crossing the           ICT files                                                                       Two shelves are 75 cm and 87 cm long.
                        hundreds boundary, e.g. 47 +                                 65 – 28 65 – 30 is 35, but this takes away 2        What is their total length in metres?
Further                 58, 101 – 35                     Problem solving             too many, so add back 2 to make 37.                 What is the difference in their lengths in
examples of             Use mental methods to add        materials:                                                                      centimetres?
pitch and               and subtract 2 or more 2, 3 or                               102 + 295 There are three hundreds and 90
expectations:           4 digit numbers-(special         Arithmagons                 and 7, that’s 397.                                  Raiza got into the pool at 2:26. She swam until
                        cases, e.g. look for number      Card tricks                                                                     3 o’clock.
Year 4                  bonds to 10/100 or count on      Esmerelda coins             500 – 180 Take away 200, that’s 300, add 20         How long did she swim?
 Further                when subtracting numbers         Crackers                    is 320.
Information             near multiples of 100, 1000,     Coin rows                                                                       find the missing number in:
- Divide and            e.g. 1995 from 6007)             Sheepdog trials             Extend to calculations that cannot entirely be      91 + ▲ + 48 = 250
rule1                                                    Three monkeys               done mentally.
                                                         Three digits                For example:                                        • find all the different totals you can make by
- Divide and                                             Add to 100                  447 + 165 447 + 100 = 547                           using three of these five numbers:
rule2                                                    More differences            547 + 60 = 607                                      219, 193, 74, 156, 97
                                                         Sum fun                     607 + 5 = 612
- teaching                                               Kierons cats                                                                    • 93 take away 8… Take 7 from 62…
mental                                                   Presents 3                  Arrange the numbers 1, 2, 3... to 9 in the          • 63 subtract 46… Subtract 120 from 215…
calculation                                              Magic square                circles so that each side of the square adds up     • 170 less than 250… 1000 less than 5437…
strategies                                               Shape puzzle                to 12.                                              • What must I take from 84 to leave 26?
                                                         Number square                                                                   • What is the difference between 28 and 65?
- teaching                                               mystery                                                                         • How many more than 234 is 249?
written
                                                                                                                                         • How many less than 68 is 42?
strategies          c                                    Snakes and ladders                                                              • What must I add to 54 to make 93?
                                                                                                                                         • Decrease 72 by 34.
- exemplification                                        Laminated empty                                                                 • 28 add a number is 43. What is the number?
of standards                                             number lines and                                                                • Find pairs of numbers with a difference of
                                                         whiteboard pens.                                                                79…

                                                                                     Solve number puzzles: for example,                  work out mentally by counting up from the
                                                                                     • Each ▲ represents a missing digit.                smaller to the larger number:
                                                                                     a. Choose three digits from this set: 1, 3, 4, 8.
                                                                                     Replace each u to make this statement true:         92 – 89,        403 – 386,        4000 – 3993
                                                                                     ▲▲ – ▲ = 38
                                                                                     b. Find the missing digits.                         Add mentally:
                                                                                     4▲ + ▲8 = 74                                        • several small numbers, such as 3 + 5 + 7 + 2
                                                                                     3▲ – ▲9 = 9                                         + 9;
                                                                                                                                         • three multiples of 10, such as 80 + 70 + 40.
                                                                                     3▲ + ▲7 = 120
                                                                                                                                         work out mentally that:
                                                                                     I think of a number, then subtract 18.
                                                                                                                                         7003 – 6988 = 15 by counting up 2 from 6988
                                                                                     The answer is 26.
                                                                                                                                         to 6990, then 10 to 7000, then 3 to 7003.
                                                                                     What was my number?
                                                                                                                                                                                 Level 3b
       Theme: Written methods for subtraction

                                                             Key Resources /
Year Target         Group Target                                                       Outcomes
                                                             Models and Images
                            Add or subtract mentally pairs   Autumn: Unit 11           Most pupils should be able to:
                            of two-digit whole numbers,      Spring: Unit 9; unit 10
Yr 5                        e.g. 47 + 58, 91 – 35            Summer: unit 11           • 3754 add 30… Add 700 to 9764…
                                                                                       • 18 add 30 add 29… Add 250, 60, 40, 150 and
                                                             Springboard 5 unit 7      3…
                            Use mental methods to add        Springboard 5 unit 8a     • What is the sum/total of 226 and 39?
Calculate                   and subtract 2 or more 2, 3 or                             • How many altogether are 121 and 345?
efficiently and             4 digit numbers-(special         ICT files                 • Increase 190 by 37.                              Write a number in each circle so that the
accurately                  cases, e.g. look for number                                • Which three numbers could have a total of        number in each square box equals the sum
                            bonds to 10/100 or count on      Problem solving           450?                                               of the two numbers on either side of it.
Further                     when subtracting numbers         materials:                Are there any others?
examples of                 near multiples of 100, 1000,                                                                                  • I cut 65 cm off 3.5 metres of rope.
pitch and                   e.g. 1995 from 6007)             Joins                                                                        How much is left?
                                                                                       Respond rapidly to oral or written questions,
expectations:               Calculate mentally with whole    Moneybags                 explaining the strategy used. For example:
                            numbers and decimals, e.g.       Three digits              • 127 take away 35… Take 80 from 373…              Dad bought a 2 kg bag of carrots.
Year 5                      U.t ± U.t                                                                                                     He used 400 grams of carrots to make some
                                                             Albert square             • 678 subtract 105… Subtract 50 from 225…
                                                             Arithmagons 2             • 500 less than 720.                               soup.
Further                                                                                                                                   How many grams of carrots
                                                             Magic square              • What must I take from 220 to leave 55?
Information                                                                                                                               were left?
                                                             Magic lines               • What is the difference between 155 and 390?
- Divide and                                                 Pyramids                  • How many more than 952 is 1050?
rule1                                                                                                                                     200 ml more water is poured
                                                             Kierons cat               • How many less than 305 is 94?
                                                             Presents 3                • What must I add to 720 to make 908?              into the cylinder.
- Divide and                                                                                                                              Mark the new water level.
                                                             Shape puzzle              • Decrease 92 by 78.
rule2
                                                                                       • 570 add a number is 620. What is the number?
                                                             Snakes and ladders        • Find pairs of numbers with a difference of
- teaching                                                                                                                                Solve addition and subtraction
                                                             Long jump challenge       599…
mental                                                       Pole climber                                                                 problems in time table context
calculation                                                  Swimming race
strategies                                                                             • 705 – 287, 8006 – 2993

                                                             Laminated empty           1.5 + 1.6 = 3.1 double 1.5 plus 0.1.
- teaching                                                   number lines and
written                                                      whiteboard pens.
strategies                                                                             Continue to add/subtract 9, 19, 29… or 11, 21,
                                                                                       31… by adding/subtracting 10, 20, 30… then
- exemplification                                                                      adjusting
of standards                                                                           by 1.
                                                                                                                                                                           • How many
                                                                                       Given the numbers 135, 228 and 363, say or                                          matches in
                                                                                       write four different sentences relating these                                       total did
                                                                                       numbers.                                                                            Rovers play?

                                                                                       Add mentally:
                                                                                       • several small numbers, such as 3 + 5 + 7 + 2 +
                                                                                       9;                                                 In how many of their matches did Rovers
                                                                                       • three multiples of 10, such as 80 + 70 + 40.     score more than 3 goals?

                                                                                                                                                                             Level 3a-4c
                    Use mental methods in special   Autumn: unit 11       Most pupils should be able to:
                                                                                                                                Calculate the third
                    cases, e.g. to subtract 1995    Spring: unit 7        • Add 4250 to 3536… 66 add 314 add 750…
Yr 6                from 6007                       Summer: unit 2;       • Add 1200, 400, 600, 1200 and 15.                       angle of a
                                                                          • What is the sum/total of 753 and 227?                  triangle, given the
                                                    Springboard unit 12   And of 93, 62 and 25?
Calculate           Calculate mentally with whole   Springboard unit 13   • How many altogether are 854 and 622?                other two.
efficiently and     numbers and decimals, e.g.                            And 91, 88 and 6?
accurately          U.t ± U.t                                             • Increase 250 by 420.
                                                    ICT files             Which three numbers could have a total of 1?
Further                                                                   Respond rapidly to oral or written questions,
examples of         Consolidate and extend
                    mental methods of calculation   Problem solving       explaining the strategy used. For example:
pitch and                                           materials:            • 750 take away 255… Take 300 from 1240…                                       Calculate angles
expectations:                                                             • 3500 subtract 2050… Subtract 2250 from 8500…
                                                                                                                                                         at a point.
                                                    Joins                 • What must I take from 8.4 to leave 2.6?
Year 6                                              Moneybags             • What is the difference between 2.2 and 6.5?
                                                    Three digits          • How much more than 23.4 is 24.9?                    Some children ran in two races on sports
Further                                             Albert square         • How much less than 6.8 is 4.2?                      day. Here are their times.
Information                                         Age old problems      • What must I add to 5.4 to make 9.3?
- Divide and                                        Franco’s fast food    • Decrease 5.6 by 1.9.
rule1                                               Make 200              • 2.8 add a number is 4.3. What is the number?
                                                    P+Q                   • Find pairs of numbers with a difference of 13.5…
- Divide and                                        Arithmagons 2
rule2                                               Magic square          • 8000 – 2785 is 15 + 200 + 5000 = 5215
                                                    Magic lines
- teaching                                          Shape puzzle          • 421 + 387 = 808
mental                                                                    double 400 plus 21 minus 13.
calculation                                         ICT games
strategies                                          Long jump challenge   Add/subtract 0.9, 1.9, 2.9… or 1.1, 2.1, 3.1…         In the 800m race, how many seconds did
                                                    Pole climber          by adding or subtracting 1, 2, 3… then adjusting      Barry finish ahead of Elise?
- teaching                                          Swimming race         by 0.1.
written                                                                                                                         The first two numbers in this sequence
strategies                                          Laminated empty       Add mentally three or more multiples of 10, such as   are 2.1 and 2.2. The sequence then
                                                    number lines and      80 + 70 + 40 + 90.                                    follows the rule ‘to get the next
- exemplification                                   whiteboard pens.                                                            number,add the two previous numbers
of standards                                                              Leon and Sara each started with different numbers.    ‘ Write in the next two numbers in the
                                                                                                                                sequence.
                                                                                                                                2.1, 2.2, 4.3, 6.5,
                                                                                                                                                                ,

                                                                                                                                Calculate the
                                                                                                                                perimeters and
                                                                                                                                areas of
                                                                                                                                compound
                                                                                                                                shapes that can
                                                                          Leon and Sara both get the same answer.               be split into
                                                                          What numbers could they have started with?            rectangles.
                                                                                                                                For example, find the perimeter /area of
                                                                          The temperature is –5 °C. It falls by 6 degrees.      this shape.
                                                                          What is the temperature now?
                                                                                                                                                                Level 4b-4a
                    Consolidate and extend          Autumn: unit 11       Some pupils could:                               Liam has two rectangular tiles like this.
                    mental methods of calculation   Spring: unit 7

                                                    Springboard unit 12
                                                    Springboard unit 13


                                                    ICT files

                                                    Problem solving
                                                                          How long does the first train from Edinburgh
                                                    materials:
Yr 6                                                                      take to travel to Inverness?
                                                    Joins                                                                  What is the perimeter of Liam’s L shape?
Further                                                                   A sequence starts at 500 and 80 is subtracted
                                                    Moneybags
examples of                                                               each time.
                                                    Three digits                                                           A drink and a box of popcorn together cost
pitch and                                           Albert square
                                                                                     500      420      340 ...             90p.
expectations:                                       Age old problems
                                                    Franco’s fast food
Year 6 into year                                                          The sequence continues in the same way.
                                                    Make 200
7                                                   P+Q
                                                                          Write the first two numbers in the sequence
                                                    Arithmagons 2
Further                                                                   which are less than zero.
                                                    Magic square                                                           2 drinks and a box of popcorn together costs
Information                                         Magic lines
                                                                          Megan makes a sequence of numbers starting       £1.45.
- Divide and                                        K+m+n
rule1                                                                     with 100.
                                                    Shape puzzle
                                                                          She subtracts 45 each time.
                                                    Laminated empty
- Divide and                                                              Write the next two numbers in the sequence.
                                                    number lines and
rule2                                               whiteboard pens.
                                                                                     100      55       10 …
                                                                                                                           What does a box of popcorn cost?
- teaching                                          Long jump challenge
mental                                                                    Calculate 15.05 – 14.84
                                                    Pole climber                                                           n stands for number. Match the equivalent
calculation                                                               Calculate 8.6 – 3.75
                                                    Swimming race                                                          expressions. One has been done for you.
strategies
                                                                          Circle the two numbers which add up to 1.
- teaching                                                                                                                     k, m and n each stand for a whole
written                                                                      0.1      0.65     0.99     0.45     0.35                      number.
strategies
                                                                          Here is a table of temperatures at dawn on the        They add together to make 1500
- exemplification                                                         same day.
of standards
                                                                                        Temperatures ºC
                                                                                                                                     k + m + n = 1500
                                                                                      London            –4º
                                                                                      Moscow            –6º                       m is three times as big as n.
                                                                                      New York          –9º
                                                                                      Paris             +6º                           k is twice as big as n.
                                                                                      Sydney           +14º
                                                                                                                               Calculate the numbers k, m and n.
                                                                          What is the difference in temperature between
                                                                          London and Paris?                                                                   level 5c-5b

				
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